Org remarks. Parts of the book which can be read: 4 th edition: Chapter 1: pages 3-31 Chapter 2: pages 35-91 Chapter 3: examples 3.4 and 3.5; pages 115-139 Chapter 4: pages 149-170 Chapter 5: pages 207-222 3d edition: Chapter 1 Chapter 2: pages 29-65; sections 2.7-2.9 - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Slide 1-1Org remarks• Parts of the book which can be read:
• CLUs: discussion of algorithms and hardware for multiplication (and discuss the idea of Booth’s algorithm)
• Sequential Circuits: Ways of clocking flip-flops
• Von Neumann Computer Model
• Implementation of the fetch-part of the eternal von Neumann cycle
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-3
An old acquaintance: processor-project assignment 1 (1.3)
Digital Techniques Fall 2007 André Deutz, Leiden University
0
1
2
3+
2
a b c_in k_1 k_0
c_out
r(esult)
1-b
it A
LU
as
spec
ifie
d in
1.3
Slide 1-4An old acquaintance: processor-project assignment 1 (1.3): 1-bit
ALU
Digital Techniques Fall 2007 André Deutz, Leiden University
0123+
2ab c_ink_1 k_0
c_out
r(esult)
Let us find another implementation Of the 1-bit ALU by constructing The Truth table for r(esult) and c_outSubsequently read off the canonical Sum of minterms for r and c_out, simplify this sum With the Quine-McCluskey Algorithm.Convert the minimized sums into LDs.
Slide 1-5
Digital Techniques Fall 2007 André Deutz, Leiden University
1-b
it A
LU
sp
ecif
ied
in 1
.3T
T f
or r
an
d c
_ou
t
Slide 1-6
Digital Techniques Fall 2007 André Deutz, Leiden University
Canonical sum for r(esult) and c_out
We continue with r:
Slide 1-7
Digital Techniques Fall 2007 André Deutz, Leiden University
Simplification of the expression for r by Quine-McCluskey
Slide 1-8
Digital Techniques Fall 2007 André Deutz, Leiden University
Simplification of the expression for r by Quine-McCluskey
Slide 1-9
Digital Techniques Fall 2007 André Deutz, Leiden University
Simplification of the expression for r by Quine-McCluskey
Slide 1-10
Digital Techniques Fall 2007 André Deutz, Leiden University
Simplification of the expression for r by Quine-McCluskey
1 0011_ v VO2 010_1 v v3 0101_ v v4 100_1 v VO5 111_1 v VO6 0_ _10 VO v v VO7 _1_01 v VO v v8 1_ _01 v VO v v9 11_0_ VO v VO v
Simplification of the expressionfor r by Quine-McCluskey
The red one are the essential prime implicants
Slide 1-13
Digital Techniques Fall 2007 André Deutz, Leiden University
Selection Table No 2 for Quine-McCluskey (for this example the last one)
m1101011
010_1 v
0101_ v
Simplification of the expression for r by Quine-McCluskey
Slide 1-14
Digital Techniques Fall 2007 André Deutz, Leiden University
prime implicants:a b c_in k_1 k_0
0 0 1 1 --- a'b'c_in k_1by selection tables we conclude: essential prime
0 1 0 --- 1 a'bc_in' k_00 1 0 1 --- a'bc_in' k_1
1 0 0 --- 1 ab'c_in' k_0by selection tables we conclude: essential prime
1 1 1 --- 1 abc_in k_0by selection tables we conclude: essential prime
0 --- --- 1 0 a' k_1 k_0'by selection tables we conclude: essential prime
--- 1 --- 0 1 b k_1' k_0by selection tables we conclude: essential prime
1 --- --- 0 1 a k_1' k_0by selection tables we conclude: essential prime
1 1 --- 0 --- ab k_1'by selection tables we conclude: essential prime
Simplification of the expressionfor r by Quine-McCluskey
Slide 1-15
Digital Techniques Fall 2007 André Deutz, Leiden University
Construction of LD for r:
Slide 1-16
A more realistic ALU
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-17
Digital Techniques Fall 2007 André Deutz, Leiden University
A more realistic ALU: the MSB slice
Slide 1-18
Digital Techniques Fall 2007 André Deutz, Leiden University
A more realistic ALU
carryOut
Slide 1-19
Digital Techniques Fall 2007 André Deutz, Leiden University
Bits have no inherent meaning: operations determine whether they are really ASCII characters, integers, floating point numbers …
The previous slide (the ALU) makes this point quite tangible! The choice of operation will determine whether the bitstrings a_3a_2a_1a_0 , b_3b_2b_1b_0 and the output bitstring result_3result_2result_1result_0 are viewed as two’s complement (numbers -8 through +7, for a 4-bit ALU) or as binary (numbers 0 through +15).
Answer to the question of Lecture #1:
Slide 1-20
Digital Techniques Fall 2007 André Deutz, Leiden University
Multiplication: towards Booth’s Algorithm
Slide 1-21
Digital Techniques Fall 2007 André Deutz, Leiden University
64 bits
64
64 bits
Shift left
Multiplication: first attempt
64
32 bits
Slide 1-22
Digital Techniques Fall 2007 André Deutz, Leiden University
Multiplication: second attempt Hardware:
Slide 1-23
Digital Techniques Fall 2007 André Deutz, Leiden University
Multiplication: second attempt
Slide 1-24
Digital Techniques Fall 2007 André Deutz, Leiden University
Multiplication: third attempt
Slide 1-25
Digital Techniques Fall 2007 André Deutz, Leiden University
Multiplication: third attempt
Slide 1-26
Digital Techniques Fall 2007 André Deutz, Leiden University
•What about signed multiplication?•easiest solution is to make both positive & remember whether to complement product when done (leave out the sign bit, run for 31 steps)•Booth’s Algorithm is more elegant way to multiply signed numbers using same hardware as before
Multiplication: Booth’s algorithm
Slide 1-27
Digital Techniques Fall 2007 André Deutz, Leiden University
Motivation for Booth’s algorithm
Slide 1-28Booth’s Algorithm Insight
Current Bit Bit to the Right Explanation Example
1 0 Beginning of a run of 1s 0001111000
1 1 Middle of a run of 1s 0001111000
0 1 End of a run of 1s 0001111000
0 0 Middle of a run of 0s 0001111000
Originally for Speed since shift faster than add for his machine
0 1 1 1 1 0beginning of runend of run
middle of run
Slide 1-29
Booth’s Algorithm
1. Depending on the current and previous bits, do one of the following:00: a. Middle of a string of 0s, so no arithmetic operations.01: b. End of a string of 1s, so add the multiplicand to the left half of the product.10: c. Beginning of a string of 1s, so subtract the multiplicand from the left half of the product.11: d. Middle of a string of 1s, so no arithmetic operation.
2. As in the previous algorithm, shift the Product register right (arith) 1 bit.
Multiplicand Product (2 x 3)0010 0000 0011 0
Multiplicand Product (2 x -3)0010 0000 1101 0
Slide 1-30
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-31
Sequential circuits
• Ways of triggering flip-flops– Whenever the clock is asserted (level sensitive)– Whenever the clock changes state (edge-
sensitive)– Capture data on one edge of the clock and
transfer it to the output of the following edge(i.e, master-slave flip-flop)
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-32
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-33
The von Neumann Model of a computer
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-34
Digital Techniques Fall 2007 André Deutz, Leiden University
A typical “desktop” system:
Slide 1-35
Digital Techniques Fall 2007 André Deutz, Leiden University
Where is the processor?
Slide 1-36
Digital Techniques Fall 2007 André Deutz, Leiden University
A look at the motherboard:
Slide 1-37
Digital Techniques Fall 2007 André Deutz, Leiden University
Basic functional blocks of a simple computer
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-38Basic functional blocks of a simple computer
• The CPU, or processor, consists of a datapath and control• The datapath performs arithmetic and logical operations
on data stored temporarily in internal registers• The control unit determines exactly what operations are
performed. It also controls acccess to memory and I/O devices
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-39Salient feature of the von Neumann Architecture
• Storage/memory structure holds both a list of instructions (= program) and data
• The list of instructions and the data are changeable, making the computer into a universal machine (as opposed to calculators).
Digital Techniques Fall 2007 André Deutz, Leiden University
Slide 1-40
Digital Techniques Fall 2007 André Deutz, Leiden University4-40